Abstract
By a stable process we mean a process X = (X(t) | t ∈ T) such that all linear combinations of the random variables X(t) have a stable distrition as defined in [5, p. 166].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Yu. K. Belayev: On the unboundedness of the sample functions of Gaussian processes. Theor. Probability Appl. 3 (1958), 327–329.
H. Cramer and M. R. Leadbetter: Stationary and Related Stochastic Processes. Wiley, New York 1967.
R. M. Dudley: Sample functions of the Gaussian process. Annals of Probability 1 (1973), 66–103.
R. M. Dudley and M. Kanter: Zero-one laws for stable measures. Proceedings Amer. Math. Soc. 45 (1944), 1–8.
W. Feller: Introduction to Probability Theory and its Applications 2. Wiley, New York 1966.
X. Fernique: Integrabilite des vecteurs gaussiens. C. R. Acad. Sci. Paris 258, (1970), 6058–6060.
M. Kanter: Linear sample spaces and stable processes. Journal of Functional Analysis 9 (1972), 441–459.
M. Kanter: A representation theorem for L p spaces. Proceedings Amer. Math. Soc. 31 (1972), 472–474.
M. Kanter: On the spectral representation for symmetric stable random variables. Z. Wahrscheinlichkeitstheorie and Verw. Gebiete 23 (1972), 1–6.
M. Kanter: Stable laws and the imbedding of L p spaces. Amer. Math. Monthly 80 (1973), 403–407.
H. J. Landau and L. A. Shepp: On the supremum of a Gaussian process. Sankhya Ser A 32 (1971), 369–378.
Lucien, Le Cam: An inequality on the concentration of sums of random variables. Ann. Math. Stat. (1962), 826.
M. Loeve: Probability Theory. 3rd ed. Van Nostrand, Princeton 1963.
G. Maruyama: The harmonic analysis of stationary stochastic processes. Mem. Fac. Sci. Kyusyu Univ. A 4, (1949), 45–106.
A. W. Roberts and D. E. Varberg: Convex Functions. Academic Press, New York (1973), p. 108.
A. V. Skorokhod: A note on Gaussian measures in a Banach space. Theory of Probability and its Applications 15, p. 508.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1977 ACADEMIA, Publishing House of the Czechoslovak Academy of Science, Prague
About this chapter
Cite this chapter
Kanter, M. (1977). On the Boundedness of Stable Processes. In: Kožešnik, J. (eds) Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, vol 7A. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9910-3_32
Download citation
DOI: https://doi.org/10.1007/978-94-010-9910-3_32
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9912-7
Online ISBN: 978-94-010-9910-3
eBook Packages: Springer Book Archive